How do you solve 10+a^2=-7a?

Jun 22, 2018

$x = - 2$ and $x = - 5$

Explanation:

Since we have a second-degree term, we know we are dealing with a quadratic, so we need to set it equal to zero to find its zeroes.

We can add $7 a$ to both sides to get

${a}^{2} + 7 a + 10 = 0$

At this point, we want to think of two numbers that sum up to the middle term ($7$) and have a product of the last term ($10$).

After some trial and error, we arrive at $5$ and $2$. This means we can factor this as

$\left(x + 5\right) \left(x + 2\right) = 0$

Setting both factors equal to zero, we get

$x = - 2$ and $x = - 5$

Hope this helps!